Question

How do you solve \[-3{{x}^{2}}-9x=0\]?

Answer 1

Hint:Take -3x common from both the terms and divide both the sides with -3 to simplify the expression. Now, write the remaining terms in the bracket and convert it into the form of a product of two terms given as \[\left( x-a \right)\left( x-b \right)\], where ‘a’ and ‘b’ are called zeroes of the polynomial. Now, substitute each term equal to 0 and find the values of x to get the answer.

Complete step by step answer:
Here, we have been provided with the quadratic equation: \[-3{{x}^{2}}-9x=0\] and we are asked to solve it. That means we have to find the values of x.
Now, clearly we can see that we have -3x common in both the terms, so taking -3x common we get,
\[\Rightarrow -3x\left( x+3 \right)=0\]
Here, since -3 is a constant so it cannot be equal to 0, so dividing both the sides with -3 to simplify the expression, we get,
\[\Rightarrow x\left( x+3 \right)=0\]
Substituting each term equal to 0, we get,
$\Rightarrow $ x = 0 or (x + 3) = 0
$\Rightarrow $ x = 0 or x = -3

Hence, the solutions of the given equations are: - x = 0 or x = -3.

Note: One can also apply the discriminant method to get the answer. In that conditions assume the coefficient of \[{{x}^{2}}\] as ‘a’, the coefficient of x as b and the constant term as c, and apply the formula: - \[x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}\] to solve for the values of x. There can be a third method also, known as completing the square method, to solve the question. Note that the discriminant formula is obtained from completing the square method. You must not divide both the sides with -3x because if you will do so then one root will be lost, i.e. x = 0.